Existing metrics for evaluating the approximation quality of generative models do so by measuring some form of distance between the generated and the true distributions [1]}. One such distance measure is the maximum mean discrepancy (MMD) which is a statistic to test whether two distributions \(\mathcal {D}^{\prime }\)  and \(\mathcal {D}\)  are different by measuring the difference of their expected function values based on samples drawn from these distributions [2]}:
\(\textstyle \text{MMD}(\mathcal {F}, \mathcal {D}^{\prime }, \mathcal {D})\! :=\! \sup _{f \in \mathcal {F}}\left(\mathbb {E}_{x \sim \mathcal {D}}[f(x)]\! - \!\mathbb {E}_{x^{\prime } \sim \mathcal {D}^{\prime }}[f(x^{\prime })]\right)\) 
